A140255 - OEIS

%I #19 Apr 27 2023 15:23:44

%S 1,3,4,5,6,7,8,7,7,9,12,10,14,11,10,9,18,11,20,12,12,15,24,13,11,17,

%T 10,14,30,15,32,11,16,21,14,15,38,23,18,15,42,17,44,18,14,27,48,16,15,

%U 15,22,20,54,15,18,17,24,33,60,20,62,35,16,13,20,21,68,24,28,19,72,19,74

%N Inverse Mobius transform of A014963.

%H Jodi Spitz, <a href="/A140255/b140255.txt">Table of n, a(n) for n = 1..5000</a>

%F A051731 as an infinite lower triangular matrix * A014963 as a vector.

%F Equals row sums of triangle A140256. - _Gary W. Adamson_, May 16 2008

%F G.f.: Sum_{k>=1} M(k)*x^k/(1 - x^k), where M(k) is the exponential of Mangoldt function (A014963). - _Ilya Gutkovskiy_, Jan 16 2017

%e a(4) = 5 = (1, 1, 0, 1) dot (1, 2, 3, 2) = (1 + 2 + 0 + 2); where (1, 1, 0, 1) = row 4 of triangle A051731 and (1, 2, 3, 2) = the first 4 terms of A014963.

%o (PARI)

%o expmangoldt(n)=ispower(n, , &n); if(isprime(n), n, 1);

%o a(n) = sumdiv(n, d, expmangoldt(d)) \\ _Jodi Spitz_, Apr 11 2023

%Y Cf. A014963, A051731, A140254.

%Y Cf. A140256.

%K nonn

%O 1,2

%A _Gary W. Adamson_ and _Mats Granvik_, May 16 2008

%E More terms from _R. J. Mathar_, Jan 19 2009